Theorems · Theorem · real analysis
ContDiffPointwiseHolderAt.fderiv
∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] {k l : ℕ} {α : ↑unitInterval} {f : E → F} {a : E},
ContDiffPointwiseHolderAt k α f a → l < k → ContDiffPointwiseHolderAt l α (fderiv ℝ f) aThe derivative of a $C^{k + (α)}$ function is a $C^{l + (α)}$ function, if l < k.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
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- unitIntervalstatement and proof · cited by 607
- Asymptotics.IsBigOproof · cited by 506
Cited by1
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- ContDiffPointwiseHolderAt.iteratedFDerivproof · cited by 0